The 24,000 members of the California Faculty Association began voting April 16 after the two sides couldn't agree on a new contract. The association includes professors, counselors and other staff across 23 campuses.
CSU has lost $970 million in state funding since 2008, which has forced the university to raise tuition, lay off employees and cut admissions.
Union leaders say they expect the members to support the strike. CSU spokesman Michael Uhlenkamp has said the administration is hopeful that a settlement can still be reached.
The Associated Press contributed to this report.